Abstract

Frequency domain methods allow us to simulate and study efficiently only some of the periodic structures that are widespread in optics and spectroscopy. Time domain approaches could be more effective, but their deployment is held back by a number of unsolved problems associated mainly with a proper truncation of the computation space in the so-called open problems. This paper is devoted to analysis of these problems in the 2-D case (infinite one-dimensionally periodic semitransparent and reflecting gratings in the field of pulsed E- and H-polarized waves).

© 2010 Optical Society of America

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  7. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).
  8. Y. K. Sirenko, S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques (Springer, 2007).
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    [CrossRef]
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    [CrossRef]
  11. P. A. Tirkas, C. A. Balanis, and R. A. Renaut, “Higher order absorbing boundary conditions for FDTD-method,” IEEE Trans. Antennas Propag. 40, 1215-1222 (1992).
    [CrossRef]
  12. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
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    [CrossRef]
  15. A. R. Maikov, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme for the Maxwell transient equations in waveguide systems,” J. Comput. Math. Math. Phys. 26, 851-863 (1986) (in Russian).
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  17. A. O. Perov, Y. K. Sirenko, and N. P. Yashina, “Explicit conditions for virtual boundaries in initial boundary value problems in the theory of wave scattering,” J. Electromagn. Waves Appl. 13, 1343-1371 (1999).
    [CrossRef]
  18. Y. K. Sirenko, V. L. Pazynin, A. I. Vyazmitinova, and K. Y. Sirenko, “Compact obstacles in free space: virtual boundaries for scalar and vector “open” initial boundary-value problems in electromagnetic wave scattering theory,” Electromag. Waves Electron. Syst. 8, 33-54 (2003) (in Russian).
  19. K. Y. Sirenko and Y. K. Sirenko, “Exact “absorbing” conditions in the initial boundary-value problems of the theory of open waveguide resonators,” Comput. Math. Math. Phys. 45, 490-506 (2005).
  20. K. Y. Sirenko, “Transport operators in the axially-symmetrical problems of the electrodynamics of pulsed waves,” Electromag. Waves Electron. Syst. 11, 15-26 (2006) (in Russian).
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    [CrossRef]
  23. K. Y. Sirenko, “Slot resonances in axially symmetric radiators of pulse-modulated and monochromatic TM0n-modes,” Telecomm. Radio Eng. 66, 9-21 (2007).
    [CrossRef]
  24. K. Y. Sirenko, “Splitting of super-broadband pulses by simple inhomogeneities of circular and coaxial waveguide,” Telecomm. Radio Eng. 67, 1425-1428 (2008).
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    [CrossRef]
  28. Y. K. Sirenko and N. P. Yashina, “Time domain theory of open waveguide resonators: canonical problems and a generalized matrix technique,” Radio Sci. 38, VIC 26-1-VIC 26-12 (2003).
    [CrossRef]
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  34. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1994).
  35. V. P. Shestopalov and Y. K. Sirenko, Dynamic Theory of Gratings (Naukova Dumka, 1989) (in Russian).
  36. Y. K. Sirenko, L. G. Velychko, and F. Erden, “Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry,” PIER 44, 57-79 (2004).
    [CrossRef]
  37. L. G. Velychko, Y. K. Sirenko, and O. S. Shafalyuk, “Time-domain analysis of open resonators. Analytical grounds,” PIER 61, 1-26 (2006).
    [CrossRef]
  38. I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).
  39. V. F. Kravchenko, V. L. Pazynin, K. Y. Sirenko, and Y. K. Sirenko, “The plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Gratings as pattern forming structures,” Electromag. Waves Electron. Syst. 14, 34-20 (2009) (in Russian).
  40. L. G. Velychko and Y. K. Sirenko, “Controlled changes in spectra of open quasi-optical resonators,” PIER B 16, 85-105 (2009).
    [CrossRef]

2009 (2)

V. F. Kravchenko, V. L. Pazynin, K. Y. Sirenko, and Y. K. Sirenko, “The plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Gratings as pattern forming structures,” Electromag. Waves Electron. Syst. 14, 34-20 (2009) (in Russian).

L. G. Velychko and Y. K. Sirenko, “Controlled changes in spectra of open quasi-optical resonators,” PIER B 16, 85-105 (2009).
[CrossRef]

2008 (2)

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

K. Y. Sirenko, “Splitting of super-broadband pulses by simple inhomogeneities of circular and coaxial waveguide,” Telecomm. Radio Eng. 67, 1425-1428 (2008).

2007 (1)

K. Y. Sirenko, “Slot resonances in axially symmetric radiators of pulse-modulated and monochromatic TM0n-modes,” Telecomm. Radio Eng. 66, 9-21 (2007).
[CrossRef]

2006 (3)

K. Y. Sirenko, “Transport operators in the axially-symmetrical problems of the electrodynamics of pulsed waves,” Electromag. Waves Electron. Syst. 11, 15-26 (2006) (in Russian).

V. L. Pazynin and K. Y. Sirenko, “The strong approach to analysis of transients in the axially symmetrical waveguide units,” Telecomm. Radio Eng. 65, 1-18 (2006).
[CrossRef]

L. G. Velychko, Y. K. Sirenko, and O. S. Shafalyuk, “Time-domain analysis of open resonators. Analytical grounds,” PIER 61, 1-26 (2006).
[CrossRef]

2005 (1)

K. Y. Sirenko and Y. K. Sirenko, “Exact “absorbing” conditions in the initial boundary-value problems of the theory of open waveguide resonators,” Comput. Math. Math. Phys. 45, 490-506 (2005).

2004 (1)

Y. K. Sirenko, L. G. Velychko, and F. Erden, “Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry,” PIER 44, 57-79 (2004).
[CrossRef]

2003 (2)

Y. K. Sirenko and N. P. Yashina, “Time domain theory of open waveguide resonators: canonical problems and a generalized matrix technique,” Radio Sci. 38, VIC 26-1-VIC 26-12 (2003).
[CrossRef]

Y. K. Sirenko, V. L. Pazynin, A. I. Vyazmitinova, and K. Y. Sirenko, “Compact obstacles in free space: virtual boundaries for scalar and vector “open” initial boundary-value problems in electromagnetic wave scattering theory,” Electromag. Waves Electron. Syst. 8, 33-54 (2003) (in Russian).

1999 (2)

A. O. Perov, Y. K. Sirenko, and N. P. Yashina, “Explicit conditions for virtual boundaries in initial boundary value problems in the theory of wave scattering,” J. Electromagn. Waves Appl. 13, 1343-1371 (1999).
[CrossRef]

Y. K. Sirenko and N. P. Yashina, “Nonstationary model problems for waveguide open resonator theory,” Electromagnetics 19, 419-442 (1999).
[CrossRef]

1996 (1)

J.-P. Berenger, “Three-dimensional perfectly matched layer for absorption of electromagnetic waves,” J. Comput. Phys. 127, 363-379 (1996).
[CrossRef]

1995 (1)

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

1994 (2)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

E. K. Miller, “Time-domain modeling in electromagnetics,” J. Electromagn. Waves Appl. 8, 1125-1172 (1994).
[CrossRef]

1992 (1)

P. A. Tirkas, C. A. Balanis, and R. A. Renaut, “Higher order absorbing boundary conditions for FDTD-method,” IEEE Trans. Antennas Propag. 40, 1215-1222 (1992).
[CrossRef]

1989 (1)

A. R. Maikov, A. D. Poezd, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme of initial boundary-value problems for Maxwell equations in unlimited domain,” J. Comput. Math. Math. Phys. 29, 239-250 (1989) (in Russian).

1986 (1)

A. R. Maikov, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme for the Maxwell transient equations in waveguide systems,” J. Comput. Math. Math. Phys. 26, 851-863 (1986) (in Russian).

1981 (1)

G. Mur, “Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

1977 (1)

B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629-651 (1977).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).

Balanis, C. A.

P. A. Tirkas, C. A. Balanis, and R. A. Renaut, “Higher order absorbing boundary conditions for FDTD-method,” IEEE Trans. Antennas Propag. 40, 1215-1222 (1992).
[CrossRef]

Bateman, H.

H. Bateman and A. Erdelyi, Tables of Integral Transforms, Vol. 1 (McGraw-Hill, 1954).

Berenger, J.-P.

J.-P. Berenger, “Three-dimensional perfectly matched layer for absorption of electromagnetic waves,” J. Comput. Phys. 127, 363-379 (1996).
[CrossRef]

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Borisov, V. V.

V. V. Borisov, Electromagnetic Fields of Transient Currents (St. Petersburg Univ. Press, 1996) (in Russian).

V. V. Borisov, Transient Fields in Waveguides (Leningrad State Univ. Press, 1991) (in Russian).

Engquist, B.

B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629-651 (1977).
[CrossRef]

Erdelyi, A.

H. Bateman and A. Erdelyi, Tables of Integral Transforms, Vol. 1 (McGraw-Hill, 1954).

Erden, F.

Y. K. Sirenko, L. G. Velychko, and F. Erden, “Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry,” PIER 44, 57-79 (2004).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1994).

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

He, S.

S. He, S. Strom, and V. Weston, Time Domain Wave-Splittings and Inverse Problems (Oxford Univ. Press, 1998).

Kingsland, D. M.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

Korn, G. A.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1961).

Korn, T. M.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1961).

Kravchenko, V. F.

V. F. Kravchenko, V. L. Pazynin, K. Y. Sirenko, and Y. K. Sirenko, “The plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Gratings as pattern forming structures,” Electromag. Waves Electron. Syst. 14, 34-20 (2009) (in Russian).

Kuzmitchev, I. K.

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

Ladyzhenskaya, O. A.

O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics (Springer-Verlag, 1985).

Lee, J. F.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

Lee, R.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

Maikov, A. R.

A. R. Maikov, A. D. Poezd, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme of initial boundary-value problems for Maxwell equations in unlimited domain,” J. Comput. Math. Math. Phys. 29, 239-250 (1989) (in Russian).

A. R. Maikov, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme for the Maxwell transient equations in waveguide systems,” J. Comput. Math. Math. Phys. 26, 851-863 (1986) (in Russian).

Majda, A.

B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629-651 (1977).
[CrossRef]

Melezhyk, P. M.

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

Miller, E. K.

E. K. Miller, “Time-domain modeling in electromagnetics,” J. Electromagn. Waves Appl. 8, 1125-1172 (1994).
[CrossRef]

Mur, G.

G. Mur, “Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

Pazynin, V. L.

V. F. Kravchenko, V. L. Pazynin, K. Y. Sirenko, and Y. K. Sirenko, “The plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Gratings as pattern forming structures,” Electromag. Waves Electron. Syst. 14, 34-20 (2009) (in Russian).

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

V. L. Pazynin and K. Y. Sirenko, “The strong approach to analysis of transients in the axially symmetrical waveguide units,” Telecomm. Radio Eng. 65, 1-18 (2006).
[CrossRef]

Y. K. Sirenko, V. L. Pazynin, A. I. Vyazmitinova, and K. Y. Sirenko, “Compact obstacles in free space: virtual boundaries for scalar and vector “open” initial boundary-value problems in electromagnetic wave scattering theory,” Electromag. Waves Electron. Syst. 8, 33-54 (2003) (in Russian).

K. Y. Sirenko and V. L. Pazynin, “Axially-symmetrical radiators of pulsed and monochromatic TM0n- and TM0n-waves,” Success Modern Radioelectron. No.4, 52-69 (2006) (in Russian).

Perov, A. O.

A. O. Perov, Y. K. Sirenko, and N. P. Yashina, “Explicit conditions for virtual boundaries in initial boundary value problems in the theory of wave scattering,” J. Electromagn. Waves Appl. 13, 1343-1371 (1999).
[CrossRef]

Poezd, A. D.

A. R. Maikov, A. D. Poezd, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme of initial boundary-value problems for Maxwell equations in unlimited domain,” J. Comput. Math. Math. Phys. 29, 239-250 (1989) (in Russian).

Rao, S. M.

S. M. Rao, Time Domain Electromagnetics (Academic, 1999).

Renaut, R. A.

P. A. Tirkas, C. A. Balanis, and R. A. Renaut, “Higher order absorbing boundary conditions for FDTD-method,” IEEE Trans. Antennas Propag. 40, 1215-1222 (1992).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1994).

Sacks, Z. S.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

Shafalyuk, O. S.

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

L. G. Velychko, Y. K. Sirenko, and O. S. Shafalyuk, “Time-domain analysis of open resonators. Analytical grounds,” PIER 61, 1-26 (2006).
[CrossRef]

Shestopalov, V. P.

V. P. Shestopalov and Y. K. Sirenko, Dynamic Theory of Gratings (Naukova Dumka, 1989) (in Russian).

Sirenko, K. Y.

V. F. Kravchenko, V. L. Pazynin, K. Y. Sirenko, and Y. K. Sirenko, “The plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Gratings as pattern forming structures,” Electromag. Waves Electron. Syst. 14, 34-20 (2009) (in Russian).

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

K. Y. Sirenko, “Splitting of super-broadband pulses by simple inhomogeneities of circular and coaxial waveguide,” Telecomm. Radio Eng. 67, 1425-1428 (2008).

K. Y. Sirenko, “Slot resonances in axially symmetric radiators of pulse-modulated and monochromatic TM0n-modes,” Telecomm. Radio Eng. 66, 9-21 (2007).
[CrossRef]

V. L. Pazynin and K. Y. Sirenko, “The strong approach to analysis of transients in the axially symmetrical waveguide units,” Telecomm. Radio Eng. 65, 1-18 (2006).
[CrossRef]

K. Y. Sirenko, “Transport operators in the axially-symmetrical problems of the electrodynamics of pulsed waves,” Electromag. Waves Electron. Syst. 11, 15-26 (2006) (in Russian).

K. Y. Sirenko and Y. K. Sirenko, “Exact “absorbing” conditions in the initial boundary-value problems of the theory of open waveguide resonators,” Comput. Math. Math. Phys. 45, 490-506 (2005).

Y. K. Sirenko, V. L. Pazynin, A. I. Vyazmitinova, and K. Y. Sirenko, “Compact obstacles in free space: virtual boundaries for scalar and vector “open” initial boundary-value problems in electromagnetic wave scattering theory,” Electromag. Waves Electron. Syst. 8, 33-54 (2003) (in Russian).

K. Y. Sirenko and V. L. Pazynin, “Axially-symmetrical radiators of pulsed and monochromatic TM0n- and TM0n-waves,” Success Modern Radioelectron. No.4, 52-69 (2006) (in Russian).

Sirenko, Y. K.

V. F. Kravchenko, V. L. Pazynin, K. Y. Sirenko, and Y. K. Sirenko, “The plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Gratings as pattern forming structures,” Electromag. Waves Electron. Syst. 14, 34-20 (2009) (in Russian).

L. G. Velychko and Y. K. Sirenko, “Controlled changes in spectra of open quasi-optical resonators,” PIER B 16, 85-105 (2009).
[CrossRef]

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

L. G. Velychko, Y. K. Sirenko, and O. S. Shafalyuk, “Time-domain analysis of open resonators. Analytical grounds,” PIER 61, 1-26 (2006).
[CrossRef]

K. Y. Sirenko and Y. K. Sirenko, “Exact “absorbing” conditions in the initial boundary-value problems of the theory of open waveguide resonators,” Comput. Math. Math. Phys. 45, 490-506 (2005).

Y. K. Sirenko, L. G. Velychko, and F. Erden, “Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry,” PIER 44, 57-79 (2004).
[CrossRef]

Y. K. Sirenko and N. P. Yashina, “Time domain theory of open waveguide resonators: canonical problems and a generalized matrix technique,” Radio Sci. 38, VIC 26-1-VIC 26-12 (2003).
[CrossRef]

Y. K. Sirenko, V. L. Pazynin, A. I. Vyazmitinova, and K. Y. Sirenko, “Compact obstacles in free space: virtual boundaries for scalar and vector “open” initial boundary-value problems in electromagnetic wave scattering theory,” Electromag. Waves Electron. Syst. 8, 33-54 (2003) (in Russian).

Y. K. Sirenko and N. P. Yashina, “Nonstationary model problems for waveguide open resonator theory,” Electromagnetics 19, 419-442 (1999).
[CrossRef]

A. O. Perov, Y. K. Sirenko, and N. P. Yashina, “Explicit conditions for virtual boundaries in initial boundary value problems in the theory of wave scattering,” J. Electromagn. Waves Appl. 13, 1343-1371 (1999).
[CrossRef]

Y. K. Sirenko, S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques (Springer, 2007).

V. P. Shestopalov and Y. K. Sirenko, Dynamic Theory of Gratings (Naukova Dumka, 1989) (in Russian).

Y. K. Sirenko, Simulation and Analysis of Transient Processes in Open Periodic, Waveguide, and Compact Resonators (EDENA, 2003) (in Russian).

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).

Strom, S.

Y. K. Sirenko, S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques (Springer, 2007).

S. He, S. Strom, and V. Weston, Time Domain Wave-Splittings and Inverse Problems (Oxford Univ. Press, 1998).

Sveshnikov, A. G.

A. R. Maikov, A. D. Poezd, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme of initial boundary-value problems for Maxwell equations in unlimited domain,” J. Comput. Math. Math. Phys. 29, 239-250 (1989) (in Russian).

A. R. Maikov, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme for the Maxwell transient equations in waveguide systems,” J. Comput. Math. Math. Phys. 26, 851-863 (1986) (in Russian).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

Tirkas, P. A.

P. A. Tirkas, C. A. Balanis, and R. A. Renaut, “Higher order absorbing boundary conditions for FDTD-method,” IEEE Trans. Antennas Propag. 40, 1215-1222 (1992).
[CrossRef]

Velychko, L. G.

L. G. Velychko and Y. K. Sirenko, “Controlled changes in spectra of open quasi-optical resonators,” PIER B 16, 85-105 (2009).
[CrossRef]

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

L. G. Velychko, Y. K. Sirenko, and O. S. Shafalyuk, “Time-domain analysis of open resonators. Analytical grounds,” PIER 61, 1-26 (2006).
[CrossRef]

Y. K. Sirenko, L. G. Velychko, and F. Erden, “Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry,” PIER 44, 57-79 (2004).
[CrossRef]

Vladimirov, V. S.

V. S. Vladimirov, Equations of Mathematical Physics (Dekker, 1971).

Vyazmitinova, A. I.

Y. K. Sirenko, V. L. Pazynin, A. I. Vyazmitinova, and K. Y. Sirenko, “Compact obstacles in free space: virtual boundaries for scalar and vector “open” initial boundary-value problems in electromagnetic wave scattering theory,” Electromag. Waves Electron. Syst. 8, 33-54 (2003) (in Russian).

Waynberg, B. R.

B. R. Waynberg, Asymptotic Methods in the Equations of Mathematical Physics (Moscow State Univ. Press, 1982) (in Russian).

Weston, V.

S. He, S. Strom, and V. Weston, Time Domain Wave-Splittings and Inverse Problems (Oxford Univ. Press, 1998).

Yakunin, S. A.

A. R. Maikov, A. D. Poezd, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme of initial boundary-value problems for Maxwell equations in unlimited domain,” J. Comput. Math. Math. Phys. 29, 239-250 (1989) (in Russian).

A. R. Maikov, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme for the Maxwell transient equations in waveguide systems,” J. Comput. Math. Math. Phys. 26, 851-863 (1986) (in Russian).

Yashina, N. P.

Y. K. Sirenko and N. P. Yashina, “Time domain theory of open waveguide resonators: canonical problems and a generalized matrix technique,” Radio Sci. 38, VIC 26-1-VIC 26-12 (2003).
[CrossRef]

Y. K. Sirenko and N. P. Yashina, “Nonstationary model problems for waveguide open resonator theory,” Electromagnetics 19, 419-442 (1999).
[CrossRef]

A. O. Perov, Y. K. Sirenko, and N. P. Yashina, “Explicit conditions for virtual boundaries in initial boundary value problems in the theory of wave scattering,” J. Electromagn. Waves Appl. 13, 1343-1371 (1999).
[CrossRef]

Y. K. Sirenko, S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques (Springer, 2007).

Comput. Math. Math. Phys. (1)

K. Y. Sirenko and Y. K. Sirenko, “Exact “absorbing” conditions in the initial boundary-value problems of the theory of open waveguide resonators,” Comput. Math. Math. Phys. 45, 490-506 (2005).

Electromag. Waves Electron. Syst. (3)

K. Y. Sirenko, “Transport operators in the axially-symmetrical problems of the electrodynamics of pulsed waves,” Electromag. Waves Electron. Syst. 11, 15-26 (2006) (in Russian).

V. F. Kravchenko, V. L. Pazynin, K. Y. Sirenko, and Y. K. Sirenko, “The plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Gratings as pattern forming structures,” Electromag. Waves Electron. Syst. 14, 34-20 (2009) (in Russian).

Y. K. Sirenko, V. L. Pazynin, A. I. Vyazmitinova, and K. Y. Sirenko, “Compact obstacles in free space: virtual boundaries for scalar and vector “open” initial boundary-value problems in electromagnetic wave scattering theory,” Electromag. Waves Electron. Syst. 8, 33-54 (2003) (in Russian).

Electromagnetics (1)

Y. K. Sirenko and N. P. Yashina, “Nonstationary model problems for waveguide open resonator theory,” Electromagnetics 19, 419-442 (1999).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

P. A. Tirkas, C. A. Balanis, and R. A. Renaut, “Higher order absorbing boundary conditions for FDTD-method,” IEEE Trans. Antennas Propag. 40, 1215-1222 (1992).
[CrossRef]

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

G. Mur, “Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

J. Comput. Math. Math. Phys. (2)

A. R. Maikov, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme for the Maxwell transient equations in waveguide systems,” J. Comput. Math. Math. Phys. 26, 851-863 (1986) (in Russian).

A. R. Maikov, A. D. Poezd, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme of initial boundary-value problems for Maxwell equations in unlimited domain,” J. Comput. Math. Math. Phys. 29, 239-250 (1989) (in Russian).

J. Comput. Phys. (2)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J.-P. Berenger, “Three-dimensional perfectly matched layer for absorption of electromagnetic waves,” J. Comput. Phys. 127, 363-379 (1996).
[CrossRef]

J. Electromagn. Waves Appl. (2)

A. O. Perov, Y. K. Sirenko, and N. P. Yashina, “Explicit conditions for virtual boundaries in initial boundary value problems in the theory of wave scattering,” J. Electromagn. Waves Appl. 13, 1343-1371 (1999).
[CrossRef]

E. K. Miller, “Time-domain modeling in electromagnetics,” J. Electromagn. Waves Appl. 8, 1125-1172 (1994).
[CrossRef]

Math. Comput. (1)

B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629-651 (1977).
[CrossRef]

PIER (1)

L. G. Velychko, Y. K. Sirenko, and O. S. Shafalyuk, “Time-domain analysis of open resonators. Analytical grounds,” PIER 61, 1-26 (2006).
[CrossRef]

PIER B (1)

L. G. Velychko and Y. K. Sirenko, “Controlled changes in spectra of open quasi-optical resonators,” PIER B 16, 85-105 (2009).
[CrossRef]

Radio Sci. (1)

Y. K. Sirenko and N. P. Yashina, “Time domain theory of open waveguide resonators: canonical problems and a generalized matrix technique,” Radio Sci. 38, VIC 26-1-VIC 26-12 (2003).
[CrossRef]

Radiophys. Electron. (1)

I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).

Telecomm. Radio Eng. (3)

V. L. Pazynin and K. Y. Sirenko, “The strong approach to analysis of transients in the axially symmetrical waveguide units,” Telecomm. Radio Eng. 65, 1-18 (2006).
[CrossRef]

K. Y. Sirenko, “Slot resonances in axially symmetric radiators of pulse-modulated and monochromatic TM0n-modes,” Telecomm. Radio Eng. 66, 9-21 (2007).
[CrossRef]

K. Y. Sirenko, “Splitting of super-broadband pulses by simple inhomogeneities of circular and coaxial waveguide,” Telecomm. Radio Eng. 67, 1425-1428 (2008).

Other (18)

O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics (Springer-Verlag, 1985).

V. S. Vladimirov, Equations of Mathematical Physics (Dekker, 1971).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).

H. Bateman and A. Erdelyi, Tables of Integral Transforms, Vol. 1 (McGraw-Hill, 1954).

B. R. Waynberg, Asymptotic Methods in the Equations of Mathematical Physics (Moscow State Univ. Press, 1982) (in Russian).

Y. K. Sirenko, Simulation and Analysis of Transient Processes in Open Periodic, Waveguide, and Compact Resonators (EDENA, 2003) (in Russian).

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1961).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1994).

V. P. Shestopalov and Y. K. Sirenko, Dynamic Theory of Gratings (Naukova Dumka, 1989) (in Russian).

Y. K. Sirenko, L. G. Velychko, and F. Erden, “Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry,” PIER 44, 57-79 (2004).
[CrossRef]

L.B.Felsen, ed., Transient Electromagnetic Fields (Springer-Verlag, 1976).

V. V. Borisov, Transient Fields in Waveguides (Leningrad State Univ. Press, 1991) (in Russian).

V. V. Borisov, Electromagnetic Fields of Transient Currents (St. Petersburg Univ. Press, 1996) (in Russian).

S. He, S. Strom, and V. Weston, Time Domain Wave-Splittings and Inverse Problems (Oxford Univ. Press, 1998).

S. M. Rao, Time Domain Electromagnetics (Academic, 1999).

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

Y. K. Sirenko, S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques (Springer, 2007).

K. Y. Sirenko and V. L. Pazynin, “Axially-symmetrical radiators of pulsed and monochromatic TM0n- and TM0n-waves,” Success Modern Radioelectron. No.4, 52-69 (2006) (in Russian).

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